Bogoliubov theory of entanglement in a Bose-Einstein condensate

We consider a Bose-Einstein condensate which is illuminated by a short resonant light pulse that coherently couples two internal states of the atoms. We show that the subsequent time evolution prepares the atoms in an interesting entangled state called a spin squeezed state. This evolution is analysed in detail by developing a Bogoliubov theory which describes the entanglement of the atoms. Our calculation is a consistent expansion in $1/\sqrt{N}$, where $N$ is the number of particles in the condensate, and our theory predict that it is possible to produce spin squeezing by at least a factor of $1/\sqrt{N}$. Within the Bogoliubov approximation this result is independent of temperature.Comment: 14 pages, including 5 figures, minor changes in the presentatio

Approximate Well-supported Nash Equilibria below Two-thirds

In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm exists. An epsilon-well-supported Nash equilibrium (epsilon-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most epsilon less than the best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee

Wnts control membrane potential in mammalian cancer cells

The Wnt signalling network determines gene transcription with free intracellular Ca2+ (urn:x-wiley:00223751:media:tjp13863:tjp13863-math-0001) and β‐catenin as major intracellular signal transducers. Despite its critical importance during development and disease, many of the basic mechanisms of Wnt signal activation remain unclear. Here we show by single cell recording and simultaneous urn:x-wiley:00223751:media:tjp13863:tjp13863-math-0002 imaging in mammalian prostate cancer cells that an early step in the signal cascade is direct action on the cell membrane potential. We show that Wnt ligands 5A, 9B and 10B rapidly hyperpolarized the cells by activating K+ current by Ca2+ release from intracellular stores. Medium‐throughput multi‐well recordings showed responses to Wnts at concentrations of 2 nm. We identify a putative target for early events as a TRPM channel. Wnts thus act as ligands for ion channel activation in mammalian cells and membrane potential is an early indicator of control of transcription

Structure of boson systems beyond the mean-field

We investigate systems of identical bosons with the focus on two-body correlations. We use the hyperspherical adiabatic method and a decomposition of the wave function in two-body amplitudes. An analytic parametrization is used for the adiabatic effective radial potential. We discuss the structure of a condensate for arbitrary scattering length. Stability and time scales for various decay processes are estimated. The previously predicted Efimov-like states are found to be very narrow. We discuss the validity conditions and formal connections between the zero- and finite-range mean-field approximations, Faddeev-Yakubovskii formulation, Jastrow ansatz, and the present method. We compare numerical results from present work with mean-field calculations and discuss qualitatively the connection with measurements.Comment: 26 pages, 6 figures, submitted to J. Phys. B. Ver. 2 is 28 pages with modified figures and discussion

Spin Squeezing in the Ising Model

We analyze the collective spin noise in interacting spin systems. General expressions are derived for the short time behaviour of spin systems with general spin-spin interactions, and we suggest optimum experimental conditions for the detection of spin squeezing. For Ising models with site dependent nearest neighbour interactions general expressions are presented for the spin squeezing parameter for all times. The reduction of collective spin noise can be used to verify the entangling powers of quantum computer architectures based on interacting spins.Comment: 7 pages, including 3 figure

HortiBot: A System Design of a Robotic Tool Carrier for High-tech Plant Nursing

Danish organic outdoor gardeners today use 50-300 hours per hectare for manual weeding. Through automatic controlling of an existing commercial machine this often heavy and costconsuming weeding will be eliminated. At the same time, a fully-automatic registration of field activities will contribute to the efficient implementation of EU directive 178/2002 concerning traceability in the primary production and thereby enhance the food-safety in the production chain. A radio controlled slope mower is equipped with a new robotic accessory kit. This transforms it into a tool carrier (HortiBot) for high-tech plant nursing for e.g. organic grown vegetables. The HortiBot is capable of passing over several parcels with visible rows autonomously based on a new commercial row detection system from Eco-Dan a/s, Denmark. This paper presents the solutions chosen for the HortiBot with regard to hardware, mechanicalelectrical interfaces and software. Further, the principles from a Quality Function Deployment (QFD) analysis was used to carry out the solicitation, evaluation and selection of most qualified design parameters and specifications attained to a horticultural robotic tool carrier. The QFD analysis provided a specific measure to evaluate each selected parameter in terms of satisfying user requirements and operational performance aspects. Based on a combination of importance rating and competitive priority ratings important user requirements include easy adaptation to field conditions in terms of row distance and parcel size, profitability, minimum crop damage during operation, and reliability. Lesser importance was attributed to affection value, attractive look, the possibility of out of season usage, and the use of renewable energy

FliPpr: A Prettier Invertible Printing System

When implementing a programming language, we often write a parser and a pretty-printer. However, manually writing both programs is not only tedious but also error-prone; it may happen that a pretty-printed result is not correctly parsed. In this paper, we propose FliPpr, which is a program transformation system that uses program inversion to produce a CFG parser from a pretty-printer. This novel approach has the advantages of fine-grained control over pretty-printing, and easy reuse of existing efficient pretty-printer and parser implementations

Stabilization of the number of Bose-Einstein condensed atoms in evaporative cooling via three-body recombination loss

The dynamics of evaporative cooling of magnetically trapped $^{87}$Rb atoms is studied on the basis of the quantum kinetic theory of a Bose gas. We carried out the quantitative calculations of the time evolution of conventional evaporative cooling where the frequency of the radio-frequency magnetic field is swept exponentially. This "exponential-sweep cooling" is known to become inefficient at the final stage of the cooling process due to a serious three-body recombination loss. We precisely examine how the growth of a Bose-Einstein condensate depends on the experimental parameters of evaporative cooling, such as the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. It is shown that three-body recombination drastically depletes the trapped $^{87}$Rb atoms as the system approaches the quantum degenerate region and the number of condensed atoms finally becomes insensitive to these experimental parameters. This result indicates that the final number of condensed atoms is well stabilized by a large nonlinear three-body loss against the fluctuations of experimental conditions in evaporative cooling.Comment: 7 pages, REVTeX4, 8 eps figures, Phys. Rev A in pres

Entanglement and Extreme Spin Squeezing

For any mean value of a cartesian component of a spin vector we identify the smallest possible uncertainty in any of the orthogonal components. The corresponding states are optimal for spectroscopy and atomic clocks. We show that the results for different spin J can be used to identify entanglement and to quantity the depth of entanglement in systems with many particles. With the procedure developed in this letter, collective spin measurements on an ensemble of particles can be used as an experimental proof of multi-particle entanglementComment: 4 pages, 2 figures, minor changes in the presentatio